Equivalence Definition and 721 Threads

FREE FALL OF BODIES 3-body problem (special case) According to the Newton's Mechanics: Let us consider a mass M of radius Ro. At a distance h from the center of this mass M, we place a spherical shell (e.g a spherical elevator) of mass m1 and radius R. Moreover, at the...

Iam not clear on how to prove a equivalence relation? I know that is has to have three properties reflexivity, symmetry, and transtivity, but I am unsure how to check. For example Iam given f is a function from z to d. R(z,d) = binary relation How do I prove that R(z,d) is a equivalence...

I feel aggravatingly close to the answer to this one, but have caved in. Using ~ for "is equivalent to" A given question reads: Given that f(x) ~ 3 - 5x + x^3, show that the equation f(x)=0 has a root x = a, where a lies in the interval 1 < a < 2. Clearly asking for the answer here...

Homework Statement If Z acts on R by n.x=n+x then R/Z is just S^1. CLaims the book But I think R/Z is (0,1) The Attempt at a Solution Any number greater than or equal to 1 is dealt with by the equivalence relation. How does the unit circle come into it? We are dealing only with one...

I need a push with the following theorem, thanks in advance. Let X and Y be normed spaces, and A : X --> Y a linear operator. A is continuous iff A is bounded. So, let A be continuous. Then it is continuous at 0, and hence, for \epsilon = 1 there exists \delta > 0 such that for all x from...

Prove x <=> y is logically equivalent to (x-->y) ^ ((~x)-->(~y)).

Gravitational "Charge" - Equivalence between Gravitational and Inertial Mass My mind is currently in a mess regarding the equivalence of gravitational mass and inertial mass. Yes, I know which comes in which equation and that they have been experimentally observed to be equal, etc., but I'm...

In a G field, clocks at a lower potential (closer to the mass producing the field) are known to run slower. When the two clocks are brought togther, the upper clock should be found to have accumulated more time than the lower clock. A rocket accelerating at "a" is equivalent to a G field...

Hello everyone. I'm reading Goldstein's Classical Mechanics (2nd Ed) and I have worked out the derivation of Euler-Lagrange equation of motion from DAlembert's Principle as described in Chapter 1 and also the Action Integral approach in Chapter 2. I want to understand the equivalence of the...

Hi, Here is my question. I need to prove the following an equivalence relation. Let A = {1,2,3,4,5} X {1.2,3,4,5} and define a relation R on A by (x1,y1)R{ x2,y2) if x1+y1=x2+y2. I am bit confused how to use the condition x1+y1=x2+y2 to prove for transitive, symmetric and reflexive properties...

Two matrices A and B are defined to be unitarily equivalent if there exists a unitary matrix P such that A = P*BP. If one is given two matrices A and B with no P, how do we know if the matrices are unitarily equivalent? I guess what I'm asking is, is it sufficient to check whether the...

Ok, I'm having trouble understanding the path-homotopy equivalence class. It's kind of blurry when they apply the operation... [f]*[g] = [f*g] ...where [f] is the path-homotopy equivalence class of f. I can see that an element in [f]*[g] is in [f*g], but not the other way around. For...

Homework Statement A vector x in R^2 is rotate twice through an angle theta (it is rotated through theta and again through theta). Find two expressions for the matrix representing this rotation. Verify that these two expressions are equivalent Homework Equations rotation matrix R=[cos...

I am writing a solution for the following problem, I hope someone can correct it, because I am not sure what I am missing. Q. V is a finite dim. vsp over K, and W is a subspace of V. Let f be a linear functional on W. Show that there exists a linear functional g on V s. t. g(w)=f(w). Ans...

How does nonlinearity of the gravitational field equations follow from the equivalence principle? I remember hearing a handwaving example of this & I'm interested in more details.

This is not an attempt at refuting the validity of relativity, i adore Einstein like most girls love their fave rock star. To me, there is a glaring discrepancy between Einstein and Newton and it behooves me, out of shear respect, to make this right in my mind. Take the very simple...

Homework Statement Prove the following statement: Let R be an equivalence relation on set A. If b is in the equivalence class of a, denoted [[a]] then [[a]]=[[b]]. Homework Equations [[a]], [[a]]=[[b]]; definition of equivalence: a relation R on a set A that is reflexive, symmetric...

Considering how the various forms of equivalence principle can lead to ambiguous discussions, I would like to know if more formal definitions for the various forms of the Equivalence Principles are available. I would consider as "formal" all definitions that could be used (formally) to check...

Were there some tests of this kind? Would that have some meaning? Would the fluid world be very strange if the EP was (somewhat) in default? Some brainstorming on fluid mechanics and the Equivalence principle, to take another point of view? Thanks, Michel

Homework Statement http://img509.imageshack.us/img509/5658/circuituz5.jpg Find the current through resistor X for V = 7V Homework Equations Thevenin equivalence? The Attempt at a Solution Right I was advised a way to do this by assuming a 1A current flows through the resistor...

What is the field F(r) with the least symmetry and which obeys lim F(r) as r --> oo = lim F(r) as r --> 0 ?

Sorry for so many questions. In Einsteins equivalence principle, it states that an observer in a close room at 1G accel would not know the difference between that or whether he was standing on the Earth. This makes fine sense to me. But it also states as well that it is independent of...

Homework Statement I have been asked to show that \exists xAP(x)\vee\exists xBP(x) is equivalent to \exists x(A\cup B)P(x) Homework Equations 1) P\rightarrow Q \equiv \neg P \vee Q 2) \neg(P\vee Q)\equiv \neg P \wedge \neg Q 3) P \vee (Q\vee R) \equiv (P\vee Q) \vee R \equiv P...

If I am asking this question, this is maybe a proof that I need a strong "back-to-the-basics". Could you give the way? Thanks, Michel

Does the "Equivalence principle" holds in QM. If we know that in QM under an "small" height so z<< R_{earth} (radius of the earth) so the QM equation is (SE): -D^{2}\Phi (z) +2m^{2}gz\Phi (z) =2mE_{n} \Phi (n) SO the wave function is just a "Airy function" and | \Phi (z) |^{2} is an...

We all know that if we break up an atom, we get a lot of energy in return. I'm having trouble visualizing what this equation actually means. Does it mean that a large amount of energy is required to bring matter together? Does it mean a large amount of energy can be converted mass? Isn't energy...

Hello, I would like to see more clearly the differences between the various forms of the equivalence principle. When reading about it on http://en.wikipedia.org/wiki/Equivalence_principle" I have the strange feeling that the difference is too small and too easily accepted to justify the...

Please excuse my ignorance re. this subject. I know that there will be an obvious answer to this question (and that it has probably been asked a thousand time before) - apologies in advance. Question is concerning e=mc2 As I understand it, the essence of this equation is that energy and...

This may be stupid question... Equivalence principle - there is no experiment in a closed laboratory to determine if the lab is accelerating or at rest in a uniform gravitational field. It seems, then, that it is a fundamental property of the universe that one can always consider themselves...

I was working on the following problem: An electron and a positron each have a mass of 9.11 x 10-31 kg. They collide and both vanish, with only electromagnetic radiation appearing after the collision. If each particle is moving at a speed of 0.30c relative to the laboratory before the...

Does anybody know how to prove the following? \sum\limits_{n=0}^{\infty} \sum\limits_{m=0}^{\infty} f(n,m) = \sum\limits_{p=0}^{\infty} \sum\limits_{q=0}^{p} f(p,p-q) f(n,m) is any function of n and m. Note the change of the limiting values on the sums.

ok i don't know why i can't grasp this and i feel so stupid... here's an example in the book which i do get... Let S denote the set of all nonempty subsets of {1, 2, 3, 4, 5}, and define a R b to mean that a \cap b not equal to \emptyset. The R is clearly reflexive and symmetric...

Well I have to prove the following statements are equivalent: a. y is a rational number b. y/3 is a rational number c. 2y+5 is a rational number So a -> b -> c -> a I'm not quite sure how you are suppose to prove something is rational however. I started like this: * y = q/r Where q &...

Hi. New to this forum. Great place. A long time ago when I first read about equivalence in relation to gravity I thought it seems too much like a coincidence. I thought if it smells like a duck, looks like a duck, and quacks like a duck, chances are its a duck. I mean what if gravity is indeed...

R = the real numbers A = R x R; (x,y) \equiv (x_1,y_1) means that x^2 + y^2 = x_1^2 + y_1^2; B= {x is in R | x>= 0 } Find a well defined bijection sigma : A_\equiv -> B like the last problem, I just can't seem to find the right way to solve this??

Z = all integers A = Z; m is related to n, means that m^2 - n^2 is even; B = {0,1} I already proved that this is a equivalence relation, but i just don't know how to; I need to find a well defined bejection sigma : A_= -> B I hope this makes sense.. i wrote it up as well as I...

I want to be able to prove that S=T \, \Leftrightarrow \, \langle Sx\,|\,x \rangle = \langle Tx\,|\,x \rangle given that S,T \in \mathcal{B(H)} and x \in \mathcal{H}. If S and T are bounded linear operators and I suppose that S = T then I have to be able to prove that \langle...

Hey guys, wasn't sure what forum to post this in. So if this is the wrong forum, I apologize. Anyway, I have a problem in Real Analysis that I can't quite get. Here it is: Let f:A->B and R is a relation on A such that xRy iff f(x) = f(y). a.) Prove R is an equivalence relation b.) Show...

[FONT=Verdana]Hi All I have a problem with Set theory. I am given to prove the following; Is the intersection of two equivalence relations itself an equivalance relation? If so , how would you characterize the equivalnce sets of the intersection? Regards, Nisha.

Question: Prove that if a Cauchy sequence x_1, x_2,... of rationals is modified by changing a finite number of terms, the result is an equivalent Cauchy sequence. All the math classes I have taken previously were computational, and my textbook contains almost no definitions. So, I...

G acts via isometries on a set X, and A,B are subsets of X. Prove that the relation A~B is an equivalence relation on subsets of X iff A and B are G-equidecomposable. I think this has to do with the Banach-Schroder theorem, but am not sure. I know it is a definition in group theory, but...

May be this is a silly question, but if one converts the nonrelativistic Schrödinger equation for a free particle to an uniformly accelerated frame, is the result the same as the Schrödinger equation for a particle within a gravitational potential? I was trying some simple calculations but did...

- Albert Einstein, Relativity: The Special and General Theory, Section 23 I'm confused about how gravity could account for all of the observations of the observer on the rotating disc. If the observer dropped a ball, he would see it fall away from the disc initially, as expected if there was...

I just want to make sure that I am doing this right or if I am on the right track. To find a map f :R ---> R so that ker f ={(x,y): x^4=y^4} pi_R: (x,y) ---> {(x,y): x^4=y^4} pi_R: x ---> {R(x): x^4 is an element in X} pi_R: Y ---> {R(y): y^4 is an element in Y} Define f: R x R --->...

Is it correct that the only way to have a theory of gravitation that fulfills the equivalence principle is to make use of a tensor as the source of gravity (and not a scalar or a vector, for example)? How can this be proven?

Here is a very interesting read on SR. Were Gould not the author, I probably would have glossed and flossed this paper. http://www.arxiv.org/abs/astro-ph/0504486 E = mc^2 Without Relativity Authors: Andrew Gould

I'm new here so this may be an old question. The equivalence principle states (roughly) that one can't distinguish between an accelerating frame and a uniform gravitational field. But an accelerated charged particle radiates. Thus the EP seems to imply that a stationary charged particle in a...

Does anyone know where to find the "direct" (not by prove they are both equal to Schrodinger formualtion )proof?

I was reading the Principle of Equivalence which says that inertial mass is equal to the gravitational mass, though I am not very clear that why it should be written as a theorem. Here is what I read and the subsequent confusions that formed :- First, to define the inertial mass, you fix a...

I've wondered about this. The book for my logic course (now done with) had no rule for creating equivalences. If you had A <--> B, by the system in the book you couldn't replace occurrences of A with B and occurrences of B with A. You'd have to break down A <--> B with material equivalence...